Use of modes in jazz..

I know that in order to play modal the harmony has to be modal as well. For example playing D dorian over a D minor chord is not playing modal.

My question is what is going on when people do this in jazz? For example I see people use D dorian over a Dmin6 chord.. is this just using accidentals to get that modal sound without actually being modal? (Being in C major using b3, b7 accidentals)

The difference between Dminor and Ddorian is the 6th- dminor has a flat 6 whereas Ddorian has a natural 6. That Dmin6 chord has the NATURAL 6 note added (dont be fooled- its only the 3RD that is minor) which matches the natural 6 of Ddorian. This is why it works

EDIT: The point of that Dmin6 chord is to draw attention to that natural 6, which is the single note which separates dorian from the other "minor" modes. This attributes to the modal sound

Jazz uses chord compatibility. That means as much as that you can pick the notes/scales that fit over the chord being played/implied at that moment. Over a Dmin6 a D dorian scale fits (because of the minor third and natural 6th), just like how you can play a D phrygian scale over a Dmb9 chord (because of the minor third and b2). You could also however play a D dorian scale over a Dm chord (actually, the natural 6th clashes less with the 5th than the minor 6th).

*Remember*, this has more to do with the scale shapes then actual modal playing.

Modal jazz uses modes for harmonic context, which means someone will pick a couple of chords that outline a specific modal feeling and then solo with the notes of that mode. Other jazz, however, uses modes as scales that provide notes to use over certain chord types. This really has nothing to do with "modes" as much as it has to do with scales. However, many of the major scale modes have notes that are useful over certain chord types, so players will often "learn their modes" in order to memorize certain scales to play over certain chords. There are also other scales that are learned to play over certain chords, such as some of the melodic minor scale modes. These can all be thought of as scales and not modes, as they aren't functioning as modes in the context in which they're used. So, for example, if I had the following progression:

Dm7-G7b5-C7-Fmaj6-Fm6-Cmaj7

I could approach it using a chord-scale approach, using a D dorian scale over the Dm7 chord (really just the C major scale, as the Dm7 is currently functioning as a ii of C, but thinking of things in terms of each individual scale is useful when the changes start moving away from the key center), a G altered scale over the G7b5, a C mixolydian scale over the C7, an F major scale over the Fmaj6, an F dorian scale over the Fm6, and then a C major scale over the Cmaj7. In theory, this is how modes are applied in jazz. In practice, you'd probably just use a C major scale over most of the progression, making a slight adjustment for the G7b5, C7, and Fm6 chords. However, it's important to have a lot of different scale shapes under your fingers so that you won't be caught off guard when an odd chord pops up now and then.